parpe3 {lmomco} | R Documentation

## Estimate the Parameters of the Pearson Type III Distribution

### Description

This function estimates the parameters of the Pearson Type III distribution given the L-moments of the data in an L-moment object such as that returned by `lmom.ub`. The L-moments in terms of the parameters are complicated and solved numerically.

For the implementation in the lmomco package, the three parameters are μ, σ, and gamma for the mean, standard deviation, and skew, respectively. Therefore, the Pearson Type III distribution is of considerable theoretical interest to this package because the parameters, which are estimated via the L-moments, are in fact the product moments. Although, these values fitted by the method of L-moments will not be numerically equal to the sample product moments. Further details are provided in the examples section of the `pmoms` function documentation.

### Usage

    parpe3(lmom,checklmom=TRUE)

### Arguments

`lmom` | A L-moment object created by `lmom.ub` or `pwm2lmom`.
`checklmom` | Should the `lmom` be checked for validity using the `are.lmom.valid` function. Normally this should be left as the default and it is very unlikely that the L-moments will not be viable (particularly in the tau_4 and tau_3 inequality). However, for some circumstances or large simulation exercises then one might want to bypass this check.

### Value

An R `list` is returned.

`type` | The type of distribution: `pe3`.
`para` | The parameters of the distribution.
`source` | The source of the parameters: “parpe3”.

### Author(s)

W.H. Asquith

### References

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105–124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

### See Also

`lmom.ub`, `lmompe3`, `cdfpe3`, `quape3`

### Examples

    lmr <- lmom.ub(rnorm(20))
    parpe3(lmr)

[Package lmomco version 0.92 Index]